Reverend Flowers, who has already apologised for doing things that were "stupid and wrong" - but without elaborating - has been suspended from the Methodist Church and by the Labour Party after being filmed in a newspaper sting allegedly trying to buy illegal drugs.

The substances said to be at the centre of the claims include cocaine and ketamine - a horse tranquilliser - used as a party drug.

Image:Len Wardle joined the Co-op's board in 2002. Pic: Co-op

The allegations against Reverend Flowers, which are the subject of a police inquiry, exacerbated pressure on Britain's biggest mutual which is having to explain the background to the bank's financial difficulties - largely a result of its merger with Britannia in 2009.

Mr Wardle said in a statement: "The recent revelations about the behaviour of Paul Flowers, the former Chair of The Co-operative Bank, have raised a number of serious questions for both the Bank and the Group.

"I led the Board that appointed Paul Flowers to lead the Bank Board and under those circumstances I feel that it is right that I step down now, ahead of my planned retirement in May next year.

"I have already made it clear that I believe the time is right for real change in our operations and our governance and the Board recently started a detailed review of our democracy.

"I hope that the Group now takes the chance to put in place a new democratic structure so we can modernise in the interests of all our members."

The Co-op confirmed Mr Wardle would be replaced by Ursula Lidbetter, currently Group deputy chair and chief executive of the Lincolnshire Co-operative Society.

Image:Paul Flowers is being investigated following the Mail On Sunday's claims

His decision was announced hours after The Co-op Group launched a fact-finding probe and a root-and-branch review of its structure after "serious and wide-ranging" allegations about Reverend Flowers, who resigned in June after three years as chair of the banking arm after a £1.5bn black hole was discovered in its finances.

The Group statement on Monday said: "Given the serious and wide-ranging nature of recent allegations, the new executive management team has started a fact-finding process to look into any inappropriate behaviour at the Co-operative Group or the Co-operative Bank and to take action as necessary.

"In addition, the board of the Co-operative Group has launched a root and branch review of the democratic structure of the organisation.

"We need to modernise to ensure that the interests of all our seven million members are properly and directly represented in the oversight of our business activities."

While announcing Mr Wardle's decision to quit, the Co-op said on Tuesday that Ms Lidbetter would chair the Group through the governance review, which will include consideration of how the Board is constituted and chaired.

The Co-op Bank discovered a massive gap in its finances following the purchase of Britannia Building Society in 2009 and abortive attempts to take on hundreds of Lloyds branches.

It faces a rescue which will see 50 branches close and investors including US hedge funds take control of 70% of the business, leaving the wider Co-operative Group with just 30% - described as a "tragedy" by former group chief executive Peter Marks.

The former Co-op bank chief executive who steered through its ill-fated merger with Britannia told MPs today it was years before anyone believed it was a "daft" idea.

David Anderson told the Treasury Select Committee he did not believe that a £550m write-off ascribed to the Britannia's commercial loans was enough on its own to sink the bank.

The scandal surrounding Reverend Flowers has intensified the focus on the bank's troubles.

Critics have questioned how he could have been appointed given his apparent lack of experience in banking and Andrew Tyrie MP, chairman of the Treasury Select Committee, has said that it was clear he was "manifestly unsuitable".

Regulators have said he went through the appropriate process when he joined the Co-op's board as a non-executive director but did not face further scrutiny when he became its chairman.

In a separate development, Labour has come under pressure to return a £50,000 donation backed by Reverend Flowers.

The donation, made by the Co-operative Group, emerged as the party suspended his membership over the drug allegatons.

Labour's leadership has since attempted to distance itself from Mr Flowers, a former councillor, after it emerged he attended a private meeting with Ed Miliband in March.